Wave Characteristics of Nanotubes Conveying Fluid Based on the Non-classical Timoshenko Beam Model Incorporating Surface Energies

The aim of this paper was to investigate the wave propagation of nanotubes conveying fluid by considering the surface stress effect. To this end, the nanotube is modeled as a Timoshenko nanobeam. According to the Gurtin–Murdoch continuum elasticity, the surface stress effect is incorporated into the governing equations of motion obtained from the Hamilton principle. The governing differential equations are solved by generalized differential quadrature method. Then, the effects of the thickness, material and surface stress modulus, residual surface stress, surface density and flow velocity on spectrum curves of nanotubes predicted by both classical and non-classical theories are studied. The first three fundamental modes including flexural, axial, and shear waves of nanotubes are considered.